Cluster mean-field theory studies of the frustrated two-dimensional quantum-mechanical [formula omitted] Heisenberg model

Abstract

The phase diagrams of the two-dimensional quantum-mechanical Heisenberg model with antiferromagnetic nearest and next-nearest neighbor exchange interaction is investigated with the cluster mean-field theory. The four different scenarios considered are the J1−J2 model with only S=1∕2 spins, the J1−J2 model with only S=1 spins, and the mixed S=1∕2 and S=1J1−J2 model. Within the ferrimagnetic J1−J2 model, two different configurations of the spin order are assumed and investigated: checkerboard-like order of the S=1∕2 and S=1 spins, and a line order, where the S=1∕2, respectively, S=1 sublattice spins are ordered along lines which itself are ordered in a periodic sequence. The phase diagrams are characterized by calculating the energy per atom E and the magnetization m=|〈Sz〉|. In the antiferromagnetic S=1∕2J1−J2 model, the quantum states and the entanglement (von Neumann entropy) are investigated as a function of J2∕J1.